In satellite communication systems or mobile communication systems, an error correction coding technique, having a large code gain, is being introduced to meet requirements for system configurations, such as reduction of the required power or the antenna size. The low density parity check code is known as an error correction code having a very large code gain and is increasingly adopted for use in a variety of communication systems and recording devices, such magnetic recording devices.
The low density parity check code does not designate a single error correction coding system, but collectively denotes an error correction code system featured in that a check matrix is sparse, that is, elements of the check matrix are mostly 0, with the number of the elements 1 being extremely small.
The low density parity check code is featured by the fact that, by using an iterative decoding system, such as a sum-product algorithm or a min-sum algorithm, with selection of a sparse check matrix, an error correction coding system can be constructed which has an extremely large code gain close to a theoretical limit (see Non-Patent Publication 1 and Non-Patent Publication 2, for instance).
The decoding apparatus for the low density parity check code performs the operation of updating a variable-to-check message by a variable-node processor and the operation of updating a check-to-variable message by a check-node processor, in alternation with each other. After updating each message a preset number of times, the estimated result of the transmission data is obtained from the check-to-variable message and the received data (see Non-Patent Publication 2 and Non-Patent Publication 3, for instance).    Non-Patent Publication 1: Robert G. Gallager, ‘Low Density Parity Check Codes’, United States, MIT Press, 1963, pp. 39-56    Non-Patent Publication 2: David J. C. MacKay, ‘Good Error-Correcting Codes Based on Very Sparse Matrices, United States, IEEE Transactions on formation Theory), Vol. 45, No. 2, March 1999, p 399-431    Non-Patent Publication 3: Jinghu Chen and Marc P. C. Fossorier, ‘Near Optimum Universal Belief Propagation Based Decoding of Low-Density Parity Check Codes’, United States, IEEE Transactions on Communications), Vol. 50, No. 3, March 2002, pp. 406-414